In 1983 Karl Popper and David Miller published an argument to the effect that probability theory could be used to disprove induction. Popper had long been an opponent of induction. Since probability theory in general, and Bayes in particular is often seen as rescuing induction from the standard objections, the argument is significant.
It is being discussed over at the Critical Rationalism site.
I don't know what this is trying to mean: "On the inductive view of probabilistic inference, B is amplified to imply that A is more probably true. This would would mean the logical consequences of A which are not also logical consequences of B should be more probable given B."
Edit: there was random other stuff here. Ignore it, I'm confused about the above.